"This was locker room banter, a private conversation that took place many years ago," the statement read.

"Bill Clinton has said far worse to me on the golf course - not even close. I apologise if anyone was offended."

For his part, Mr Bush said he was "embarrassed and ashamed" at the contents of the video.

"It's no excuse, but this happened 11 years ago - I was younger, less mature, and acted foolishly in playing along. I'm very sorry."

Analysis by BBC North America reporter Anthony Zurcher

Image copyrightAP

Donald Trump has often found himself in hot water for public comments he's made about women over the years. It turns out he's said lewd and disparaging things in private as well. Go figure.

The videotape release comes at a most inopportune time for the Republican nominee, who was trying to use his running mate's well-received debate performance on Tuesday to reboot his campaign after a week of distractions and controversy. On Wednesday he told a local news interviewer that his previous offensive comments about women - which have dogged his campaign since the first Republican primary debate last August - were made for the "purpose of entertainment".

That explanation doesn't fit with the boorish, newly married Trump shown on the video privately boasting about his efforts to seduce a married woman and have his way with whomever he pleases.

Now Mr Trump will enter Sunday's debate with a new cloud hanging over his candidacy. It's almost certain that one of the town hall participants will ask him about it. There may be no easy way to respond - but Mr Trump will have to find an acceptable answer. If he bungles it, everything else he says during the 90-minute debate won't matter.

Hillary Clinton described the comments as "horrific".

"We cannot allow this man to become president," she posted on Twitter.

Mr Trump has said he will not bring up stories about Bill Clinton's infidelities in this Sunday's US presidential debate after previously threatening to do so.

House Speaker Paul Ryan said: "I am sickened by what I heard today.

"I hope Mr Trump treats this situation with the seriousness it deserves and works to demonstrate to the country that he has greater respect for women than this clip suggests."